The angle bisector of an angle divides the angle into two angles with equal measure. In the diagram below, \(A\) is on segment \(\overline{CE}\) and \(\overline{AB}\) bisects \(\angle CAD\). If we have \(\overline{DA}\parallel\overline{EF}\) and \(\angle AEF\) is \(12^\circ\) less than 10 times \(\angle BAC\), then what is \(\angle CAD\) in degrees?

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